Effectiveness factors experimental values

The mass transport influence is easy to diagnose experimentally. One measures the rate at various values of the Thiele modulus the modulus is easily changed by variation of R, the particle size. Cmshing and sieving the particles provide catalyst samples for the experiments. If the rate is independent of the particle size, the effectiveness factor is unity for all of them. If the rate is inversely proportional to particle size, the effectiveness factor is less than unity and

experimental points allow triangulation on the curve of Figure 10 and estimation of Tj and ( ). It is also possible to estimate the effective diffusion coefficient and thereby to estimate Tj and ( ) from a single measurement of the rate (48). 

The calculated energy of interaction of an atomic moment and the Weiss field (0.26 uncoupled conduction electrons per atom) for magnetic saturation is 0.135 ev, or 3070 cal. mole-1. According to the Weiss theory the Curie temperature is equal to this energy of interaction divided by 3k, where k is Boltzmann s constant. The effect of spatial quantization of the atomic moment, with spin quantum number S, is to introduce the factor (S + 1)/S that is, the Curie temperature is equal to nt S + l)/3Sk. For iron, with 5 = 1, the predicted value for the Curie constant is 1350°K, in rough agreement with the experimental value, 1043°K. 

A number of empirical methods exist for the adjustment of covalent bond lengths for ionic effects.34,35 These are based primarily on formulas that involve the sum of the covalent radii corrected by a factor that is dependent on the electronegativity difference between the atoms. In many instances, quite good agreement is obtained between the predicted and experimental values, as shown by the listing in Table I. 

The measured value of k Sg is 0.716 cm3/(sec-g catalyst) and the ratio of this value to k ltTueSg should be equal to our assumed value for the effectiveness factor, if our assumption was correct. The actual ratio is 0.175, which is at variance with the assumed value. Hence we pick a new value of rj and repeat the procedure until agreement is obtained. This iterative approach produces an effectiveness factor of 0.238, which corresponds to a differs from the experimental value (0.17) and that calculated by the cylindrical pore model (0.61). In the above calculations, an experimental value of eff was not available and this circumstance is largely responsible for the discrepancy. If the combined diffusivity determined in Illustration 12.1 is converted to an effective diffusivity using equation 12.2.9, the value used above corresponds to a tortuosity factor of 2.6. If we had employed Q)c from Illustration 12.1 and a tortuosity factor of unity to calculate eff, we would have determined that rj = 0.65, which is consistent with the value obtained from the straight cylindrical pore model in Illustration 12.2. 

The following illustration indicates how experimental and calculated values of catalyst effectiveness factors may be determined for a specific case. 

The AEGL-1 concentration was based on a 1-hour (h) no-effect concentration of 8,000 parts per million (ppm) in healthy human subjects (Emmen et al. 2000). This concentration was without effects on pulmonary function, respiratory parameters, the eyes (irritation), or the cardiovascular system. Because this concentration is considerably below that causing any adverse effect in animal studies, an intraspecies uncertainty factor (UF) of 1 was applied. The intraspecies UF of 1 is supported by the absence of adverse effects in therapy tests with patients with severe chronic obstructive pulmonary disease and adult and pediatric asthmatics who were tested with metered-dose inhalers containing HFC-134a as the propellant. Because blood concentrations in this study approached equilibrium following 55 minutes (min) of exposure and effects are determined by blood concentrations, the value of 8,000 ppm was made equivalent across all time periods. The AEGL-1 of 8,000 ppm is supported by the absence of adverse effects in experimental animals that inhaled considerably higher concentrations. No adverse effects were observed in rats exposed at 81,000 ppm for 4 h (Silber and Kennedy 1979) or in rats exposed... 

The effect of switching times on the two factors can be inferred from Pig. 23. For non-polarized sequences, we have v p = [mex(oo) — 7nex(0)]/mex(oo) which is always smaller than the theoretical value of 1. This is also true for prepolarized sequences, since it can be easily seen that the experimental value Ypp = [Mex(0) — Mex(oo)]/Mex(0) is again smaller than the theoretical value. 

Fig. 39 Plots showing the effect of surface area factor on the extent of property improvement. Symbols represent experimental values, and the lines are their apparent fitting. Encircled data points are taken from unpublished research work on NR latex-based NA nanocomposites. Vertical dotted line indicates the critical point...

These place a positive charge on the oxygen atom of the unionized molecule, and so cause it to repel the proton. On analysis of the experimental values for Ka at 25°C it is found that the inductive effect of a nitro group increases Ka by a factor of about 45, and the resonance effect in the ortho and para positions gives another factor of about 22. The acid constant of a nitrophenoi can be found approximately by multiplying that for phenol, l.t X 10 10, by the factor 45 for every meta nitro group and 1000 for every ortho or para nitro group in the molecule. The comparison of the values calculated in this way with those found by experiment is shown in Table 8-1. ... 

For the DTO model we must have an estimate of the torsional vibration frequency and the barrier to internal rotation of the constituent monomers. The DTO model fits the experimental data for bulk polymer if H = 5.4 kcal/mole, vt — 1012 c.p.s., and Zt = 30 which are not unreasonable values. One would expect the barrier height to decrease upon dilution (if it changes at all) as the chain environment loosens up. Assuming that rotation about C—O—C bonds is predominate, we take the experimental values of H = 2.63 kcal/mole, vt = 7.26 x 1012 c.p.s. of Fateley and Miller (14) for dimethyl ether. Eq. (2.8) predicts rSJ° = 0.47 X 10-8 sec at 253° K with Zt = 30. We shall use this as our dilute solution result. [The methyl pendant in polypropylene) oxide will act to increase the barrier height due to steric effects, making this calculated relaxation time somewhat low for this choice of a monomer analog.] Tmax is seen to change only by a factor of 102—103 upon dilution in the DTO model. 

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